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At a point on the ground 15 ft from the base of a​ tree, the distance to the top of the tree is 1 ft more than 2 times the height of the tree. find the height of the tree.

Respuesta :

grethantish
The height and the distance from base (15 feet) are 2 legs of a right triangle.
The hypotenuse is distance from the point 15 ft from base to top of tree,
or 2(height) + 1ft.
.
Let a=height; b=distance from base=15 ft; c=hypotenuse=2a+1ft

a2 +b2=c2 (2 means square eg:a square +b square)

a2+(15ft)2=(2a + 1ft)2
a2+225ft2=4a2 +4a+1
0=3a+4a-224
0=(a-8)-(3a+28)
a-8=0 OR 3a +28=0
a=8 OR 3a=-28
a=8 OR a=28÷3

so a=8 ft

the height of the tree is 8ft

The height of the tree is 8  feet.

Given

The distance to the top of the tree is 1 ft more than 2 times the height of the tree.

The ground is 15 ft from the base of a​ tree.

Pythagoras theorem;

The square of the length of the hypotenuse is equal to the sum of squares of the lengths of the other two sides of the right-angled triangle.

Let, the height of the is h.

The distance to the top of the tree is 1 ft more than 2 times the height of the tree.

= 2h+1

The height of the tree is given by the following formula;

[tex]\rm \text{(Height of the tree)}^2+(Ground\ from \ base \ of \ tree)^2=(Distance \ top \ of \ tree)\\\\h^2+(15^2)=(2h+1)^2\\\\h^2+225=4h^2+4h+1\\\\4h^2+4h+1-h^2-225=0\\\\3h^2+4h-224=0\\\\ 3h^2-24h+28h-224=0\\\\ 3h(h-8)28(h-8)=0\\\\(h-8)(3h+28)\\\\h-8=0, \ h=8\\\\3h+28=0, \ 3h=-28, \ h=\dfrac{-28}{3}][/tex]

The height can not be negative so the value of h is 8.

Hence, the height of the tree is 8  feet.

To know more about Pythagoras theorem click the link given below.

https://brainly.com/question/10597804

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